The present invention generally relates to scaling optical aberration measurements of optical systems. More particularly, the invention relates to improved methods and systems for processing optical power measurements taken at a first plane and converting those power measurements to corrective optical power measurements that can be used at a second plane. The present invention may be useful in any of a variety of ocular treatment modalities, including ablative laser eye surgery, contact lenses, spectacles, intraocular lenses, and the like.
Known laser eye surgery procedures generally employ an ultraviolet or infrared laser to remove a microscopic layer of stromal tissue from the cornea of the eye. The laser typically removes a selected shape of the corneal tissue, often to correct refractive errors of the eye. Ultraviolet laser ablation results in photodecomposition of the corneal tissue, but generally does not cause significant thermal damage to adjacent and underlying tissues of the eye. The irradiated molecules are broken into smaller volatile fragments photochemically, directly breaking the intermolecular bonds.
Laser ablation procedures can remove the targeted stroma of the cornea to change the cornea's contour for varying purposes, such as for correcting myopia, hyperopia, astigmatism, and the like. Control over the distribution of ablation energy across the cornea may be provided by a variety of systems and methods, including the use of ablatable masks, fixed and moveable apertures, controlled scanning systems, eye movement tracking mechanisms, and the like. In known systems, the laser beam often comprises a series of discrete pulses of laser light energy, with the total shape and amount of tissue removed being determined by the shape, size, location, and/or number of laser energy pulses impinging on the cornea. A variety of algorithms may be used to calculate the pattern of laser pulses used to reshape the cornea so as to correct a refractive error of the eye. Known systems make use of a variety of forms of lasers and/or laser energy to effect the correction, including infrared lasers, ultraviolet lasers, femtosecond lasers, wavelength multiplied solid-state lasers, and the like. Alternative vision correction techniques make use of radial incisions in the cornea, intraocular lenses, removable corneal support structures, and the like.
Known corneal correction treatment methods have generally been successful in correcting standard vision errors, such as myopia, hyperopia, astigmatism, and the like. However, as with all successes, still further improvements would be desirable. Toward that end, wavefront measurement systems are now available to accurately measure the refractive characteristics of a particular patient's eye. One exemplary wavefront technology system is the VISX WaveScan® System, which uses a Hartmann-Shack wavefront lenslet array that can quantify aberrations throughout the entire optical system of the patient's eye, including first- and second-order sphero-cylindrical errors, coma, and third and fourth-order aberrations related to coma, astigmatism, and spherical aberrations.
Wavefront-driven vision correction has become a top choice for higher quality vision, after a series of significant development in the research of the wavefront technology (Liang, J. et al., J. Opt. Soc. Am. A 11:1949-1957 (1994); Liang, J. et al., J. Opt. Soc. Am. A 14:2873-2883 (1997); Liang, J. et al., J. Opt. Soc. Am. A 14:2884-2892 (1997); Roorda, A. et al., Nature 397:520-522 (1999)). Although the ocular aberrations can be accurately captured, several factors need to be considered when they are corrected using, say, the refractive surgical technique. The first of such factors is the relative geometric transformation between the ocular map when the eye is examined and the ocular map when the eye is ready for laser ablation. Not only can the eye have x- and y-shift between the two maps, but it can also have possible cyclo-rotations (Walsh, G. Ophthal. Physiol. Opt. 8:178-182 (1988); Wilson, M. A. et al., Optom. Vis. Sci. 69:129-136 (1992); Donnenfeld, E. J. Refract. Surg. 20:593-596 (2004) Chernyak, D. A. J. Cataract. Refract. Surg. 30:633-638 (2004)). Such problems have been studied by Guirao et al. (Guirao, A. et al., J. Opt. Soc. Am. A 18:1003-1015 (2001)). Another problem deals with the pupil size change (Goldberg, K. A. et al., J. Opt. Soc. Am. A 18:2146-2152 (2001); Schwiegerling, J. J. Opt. Soc. Am. A 19:1937-1945 (2002); Campbell, C. E. J. Opt. Soc. Am. A 20:209-217 (2003)) using Zernike representation (Noll, R. J. J. Opt. Soc. Am. 66:203-211 (1976); Born, M. et al., Principles of Optics, 7th ed. (Cambridge University Press, 1999)). Because of the analytical nature and the popularity of Zernike polynomials, this problem has inspired an active research recently (Dai, G.-m. J. Opt. Soc. Am. A 23:539-543 (2006); Shu, H. et al., J. Opt. Soc. Am. A 23:1960-1968 (2006); Janssen, A. J. E. M. et al., J. Microlith., Microfab., Microsyst. 5:030501 (2006); Bará, S. et al., J. Opt. Soc. Am. A 23:2061-2066 (2006); Lundström, L. et al., J. Opt. Soc. Am. A (accepted)).
Wavefront measurement of the eye may be used to create a high order aberration map or wavefront elevation map that permits assessment of aberrations throughout the optical pathway of the eye, e.g., both internal aberrations and aberrations on the corneal surface. The aberration map may then be used to compute a custom ablation pattern for allowing a surgical laser system to correct the complex aberrations in and on the patient's eye. Known methods for calculation of a customized ablation pattern using wavefront sensor data generally involves mathematically modeling an optical surface of the eye using expansion series techniques. More specifically, Zernike polynomials have been employed to model the optical surface, as proposed by Liang et al., in Objective Measurement of Wave Aberrations of the Human Eye with the Use of a Hartmann-Shack Wave-front Sensor, Journal Optical Society of America, July 1994, vol. 11, No. 7, pp. 1949-1957, the entire contents of which is hereby incorporated by reference. Coefficients of the Zernike polynomials are derived through known fitting techniques, and the refractive correction procedure is then determined using the shape of the optical surface of the eye, as indicated by the mathematical series expansion model.
There is yet another problem that remains unaddressed. Optical measurements such as wavefront measurements are often taken at a measurement plane, whereas optical treatments may be needed at a treatment plane that is different from the measurement plane. Thus, power adjustments are often used when devising optical treatments for patients. For example, power adjustments can be used by optometrists when prescribing spectacles for patients. Typically, refractive measurements are made by an optometer at a measurement plane some distance anterior to the eye, and this distance may not coincide with the spectacle plane. Thus, the measured power corresponding to the measurement plane may need to be converted to a corrective power corresponding to the spectacle or treatment plane. Similarly, when wavefront measurements are obtained with wavefront devices, in many cases the measured map is conjugated to the pupil plane, which is not the same as the corneal plane or spectacle plane. To enhance the effectiveness of a refractive surgical procedure, vertex correction may be needed to adjust the power of the measured maps. Yet there remains a lack of efficient methods and systems for such power conversions. In other words, when the ocular aberrations are captured, they are often on the exit pupil plane. However, when the correction is applied, it is often on a different plane. For example, for refractive surgery, it is on the corneal plane. For contact lens, it is on the anterior surface of the contact lens. For intraocular lens, it is on the lens plane. And for spectacles, it is on the spectacle plane. Traditionally, for low order spherocylindrical error, a vertex correction formula can be applied (Harris, W. F. Optom. Vis. Sci. 73:606-612 (1996); Thibos, L. N. S. Afr. Optom. 62:111-113 (2003)), for example, to archive the power correction for the so-called conventional treatment for refractive surgery. The same formula can be applied to the power calculation for vision correction using the contact lens, intraocular lens, and spectacles. However such formulas may not be useful in some cases, for example where there are high order ocular aberrations to be corrected. Hence, new formulas are needed to represent the ocular aberrations when they are propagated to a new plane.
Therefore, in light of above, it would be desirable to provide improved methods and systems for processing optical data taken at a measurement plane and converting that optical data to corrective optical data that can be used at a treatment plane.